Wealth Effect on Portfolio Allocation in Incomplete Markets

76 Pages Posted: 22 Apr 2020 Last revised: 19 Mar 2024

See all articles by Chenxu Li

Chenxu Li

Peking University - Guanghua School of Management

O. Scaillet

Swiss Finance Institute - University of Geneva

Yiwen Shen

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management

Yueting Jiang

The Chinese University of Hong Kong (CUHK) - CUHK Business School

Date Written: March 10, 2024

Abstract

In this paper, we develop a novel decomposition of optimal dynamic portfolio choice under flexible incomplete market models and the wealth-dependent HARA utility. The decomposition reveals the fundamental impacts from market incompleteness and wealth effect in portfolio allocation. With hedgeable interest rate risk, the optimal portfolio under HARA utility can be decomposed to a pure CRRA optimal portfolio and a financing portfolio for the investor’s future subsistence requirements. In this case, the wealth growth rate is always higher for HARA investors with higher initial wealth levels, leading to increased wealth inequality. As an application of our decomposition, we solve the HARA optimal policy in closed-form under an incomplete market model with both stochastic interest rate and volatility. Using parameters calibrated from U.S. market data, we find that the wealth effect generates a procyclical pattern in investor’s stock positions and time varying risk aversion levels in different market regimes. Moreover, we identify a novel “buy-high-sell low” effect that may hurt the HARA investors with low initial wealth.

Keywords: optimal portfolio choice, incomplete market, wealth-dependent utility, closed-form analysis, wealth inequality, heterogenous investors.

JEL Classification: C61, C63, G11

Suggested Citation

Li, Chenxu and Scaillet, Olivier and Shen, Yiwen and Jiang, Yueting, Wealth Effect on Portfolio Allocation in Incomplete Markets (March 10, 2024). Swiss Finance Institute Research Paper No. 20-22, Available at SSRN: https://ssrn.com/abstract=3580735 or http://dx.doi.org/10.2139/ssrn.3580735

Chenxu Li

Peking University - Guanghua School of Management ( email )

Guanghua School of Management
Beijing, 100871
China

Olivier Scaillet (Contact Author)

Swiss Finance Institute - University of Geneva ( email )

Geneva
Switzerland

Yiwen Shen

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management ( email )

Clear Water Bay
Kowloon
Hong Kong

Yueting Jiang

The Chinese University of Hong Kong (CUHK) - CUHK Business School ( email )

Cheng Yu Tung Building
12 Chak Cheung Street
Shatin, N.T.
Hong Kong

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